In this contribution we derive an expression of the Cramér-Rao bound for hybrid cooperative positioning, where GNSS information is combined with terrestrial range measurements through exchange of peer-to-peer messages. These results provide a theoretical characterization of achievable performance of hybrid positioning schemes, as well as allow to identify critical network configurations and dev...

Recently, Direct Position Estimation (DPE) has arisen as a potential approach to deal with the positioning problem in Global Navigation Satellite System receivers. The conventional navigation solution is obtained in two steps: synchronization parameters are estimated and then a trilateration procedure is in charge of computing user’s position, based on those parameters. In contrast, DPE estimat...

Despite an increased interest in complex independent component analysis (ICA) during the last two decades, a closed-form expression for the Cramér-Rao bound (CRB) of the complex ICA problem has not yet been established. In this paper, we fill this gap for the noiseless case and circular sources. The CRB depends on the distributions of the sources only through two characteristic values which can...

In some point estimation problems, we may confront imprecise (fuzzy) concepts. One important case is a situation where all observations are fuzzy rather than crisp. In this paper, using fuzzy set theory, we define a fuzzy-valued random variable, a fuzzy unbiased estimator, a fuzzy exponential family, and then we state and prove a Cramér-Rao lower bound for such fuzzy estimators. Finally, we giv...

Salazar, Dunn and Graham in [15] presented an improved Feng-Rao bound for the minimum distance of dual codes. In this work we take the improvement a step further. Both the original bound by Salazar et. al., as well as our improvement are lifted so that they deal with generalized Hamming weights. We also demonstrate the advantage of working with one-way well-behaving pairs rather than weakly wel...

Cramér-Rao lower bounds (CRLBs) are proposed for deterministic parameter estimation under model mismatch conditions where the assumed data model used in the design of the estimators differs from the true data model. The proposed CRLBs are defined for the family of estimators that may have a specified bias (gradient) with respect to the assumed model. The resulting CRLBs are calculated for a lin...

In image reconstruction and restoration, there exists an inherent tradeoff between the recovered spatial resolution and statistical variance: lower variance can be bought at the price of decreased spatial resolution. This tradeoff can be captured for a particular regularized estimator by tracing out the resolution and variance as a curve indexed by the estimator’s smoothing parameter. When the ...

This paper presents an analysis of Cramer-Rao lower bounds (CRLB) in the phase retrieval problem. Previous papers derived Fisher Information Matrices for the phaseless reconstruction setup. Two estimation setups are presented. In the first setup the global phase of the unknown signal is determined by a correlation condition with a fixed reference signal. In the second setup an oracle provides t...

We have studied a sea navigation method relying on a digital underwater terrain map and sonar measurements. The method is applicable for both ships and underwater vessels. We have used experimental data to build an underwater map and to investigate the estimation performance. Since the problem is non-linear, due to the measurement relation, we apply a sequential Monte Carlo method, or particle ...

How accurately can one estimate a deterministic parameter subject to other unknown deterministic model parameters? The most popular answer to this question is given by the Cramér-Rao bound (CRB). The main assumption behind the derivation of the CRB is local unbiased estimation of all model parameters. The foundations of this work rely on doubting this assumption. Each parameter in its turn is t...